The double-valued coreps of \({\cal G}\)  can be obtained from the double-valued irreducible representations (irreps) of \(\mathbb {G}\) , with the results listed in Table REF .
All the coreps are 2D, except \((\Gamma _6^\pm ,\Gamma _7^\pm )\)  for \(\mathbb {G}=\mathbf {T}_{h}\)  and \(\Gamma _8^\pm \)  for \(\mathbb {G}=\mathbf {O}_{h}\) ,
which are four-dimensional. These latter coreps correspond to the bands which are fourfold degenerate at the \(\Gamma \)  point, e.g., the \(\Gamma _8^\pm \)  (“\(j=3/2\) ”) bands
in cubic crystals (Ref. Lutt56), and are not considered here. Pairs of complex conjugate irreps \((\Gamma ,\Gamma ^*)\)  produce coreps of the “pairing” type of twice the dimension,
while the 1D irreps \(\Gamma _2^\pm \)  of \(\mathbf {C}_{i}\)  and \(\Gamma _6^\pm \)  of \(\mathbf {C}_{3i}\)  produce 2D coreps of the “doubling” type.[1]}
